An energy function for transversely-isotropic elastic material and the Ponyting Effect

On the basis of the semi-linear material of John, invoking the theory of homogenization for heterogeneous media and the theory of invariants for isotropic scalar functions, an energy function is built for a transversely-isotropic medium in finite elastic deformation. The Ponyting Effect, for material in simple shear, is reviewed for this case of transversal isotropy. It is shown that this effect is apprehended by the constructed energy function.     

Degree of deformation and strength of compact bone tissue during torsion

This paper discusses the variation in the deformation and strength properties of compact bone tissue during torsion in various zones of the cross section of human tibia. A correlation has been found between the specific energy of deformation consumed during the loading process and the level of stress attained. The degree of correlation between the deformation and strength properties of the bone tissue has been studied as a function of the concentration of certain biochemical substances in its composition.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 911–918, September–October, 1973.     

Theoretical study and numerical simulation of textiles

We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically motivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural configuration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes. We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.     

The small anisotropy formulation of elastic deformation

The specific internal energy defines the constitutive relation (stress-strain function) in elastic deformations. We introduce a form for the specific internal energy that expresses the idea of small anisotropy. In this formulation, only one parameter is needed to specify the anisotropic part of the deformation.Supported in part by AFOSR-88-0025.     

研究金属中激波构造与衰减的一个物理模型

本文给出了研究金属中激波构造与衰减的一个物理模型.为了建立高速形变下材料的本构方程和研究激波过渡带的构造,需要考虑二个独立的理论方面.首先,将比内能分解成弹性压缩能和弹性形变能,而将形变能作为弹性应变和熵的函数展开到三阶项,其中考虑了热与机械能的耦合效应.其次,从位错动力学角度建议了一个塑性松弛函数以便描述高温、高压下塑性流动的特性.另外,本文给出了一个常微分方程组用以计算定态激波过渡带中各状态变量的分布以及激波的厚度.倘若假定在激波上熵的跳跃可以忽略,并用Hugoniot压缩模量代替等熵压缩摸量,可以获得一个分析解.最后,本文还提出了求解平板对称碰撞中激波波头衰减的一个近似方法。     

横观各向同性多孔超弹性矩形板的单向拉伸

利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.     

One-dimensional discrete LQR control of compression of the human chest impulsively loaded by fast moving point mass

This paper uncovers some interesting extension of an optimal discrete control methodology partially included in Proceedings and presented at the international conference on “Dynamical Systems Theory and Applications”. There has been applied a scheme for realisation of active control strategy with numerically estimated linear optimal quadratic index of performance in reduction of impact-induced deformation of human chest loaded by a point mass at the central point of upper-torso body. We focused on application of one active element attached between torso’s upper back (looking from posterior direction) and a fixed support. As the practical result we provide values of quality and reaction matrices, some useful deformation and energy dissipation time-characteristics and the resulting shape of control force time-characteristics that would be the demanding one for a hypothetical real implementation.     

静脉壁的力学特性及负压失稳问题

应用一类超弹性应变能函数,通过非线性弹性理论,研究了静脉壁在跨壁压及轴向拉伸联合作用下的变形和应力分布等力学特性,并分析了静脉壁的负压失稳问题．首先利用超弹性材料薄壁圆筒模型,得到了静脉壁在跨壁压及轴向拉伸联合作用下的变形方程,给出了正常静脉压下静脉壁的变形曲线和应力分布曲线,讨论了静脉壁的变形和应力分布规律．然后给出了负跨壁压下静脉壁的变形曲线,并由能量比较讨论了静脉壁的负压失稳问题．     

Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy

A three-dimensional thermoviscoelastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multi-dimensional, nonconvex, and nonisothermal problems is that no regularizing higher-order terms are introduced. The mechanical dissipation is not linearized. We prove existence global in time. The approach is based on a fixed-point argument using an implicit time discretization and the theory of renormalized solutions for parabolic equations with L¹ data.     

Numerical simulation of shear band formation in hyperelastic material by energy relaxation

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro-structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo-Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The equations of elastostatics in a Riemannian manifold

To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts that the deformation of the elastic body arising in response to given loads minimizes over a specific set of admissible deformations the total energy of the elastic body, defined as the difference between the strain energy and the potential of the loads. Assuming that the strain energy is a function of the metric tensor field induced by the deformation, we first derive the principle of virtual work and the associated nonlinear boundary value problem of nonlinear elasticity from the expression of the total energy of the elastic body. We then show that this boundary value problem possesses a solution if the loads are sufficiently small (in a sense we specify).     

The conservation energy principle in description of stable and unstable states for aluminium

In the paper the physical model based on the energy conservation principle is proposed. On the basis of this principle the division of energy on volumetric and deviatory parts is presented. In this model a concept of energy division is recognised as important. Using the strain energy density function we can formulate criteria of the material equilibrium stability. Considerations are carried out for aluminium. All assumptions are based on uniaxial tension test supported by transverse deformation measurements. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

不可压缩橡胶类材料裂纹尖端应力应变场*

本文对平面应变情况下不可压缩橡胶类材料裂纹尖端弹性场进行了有限变形分析.裂纹尖端场被分为收缩区和扩张区.借助于新的应变能函数和变形模式,推出了尖端场各区的渐近方程,得到了尖端场的完整描述.本文对奇异性作了讨论,得到了不可压缩橡胶类材料裂纹尖端应力及应变分布曲线,揭示了裂纹尖端应力应变场的特性.     

活体大变形的能量原理

活体是具有自组织和自调控能力的生命系统.讨论活体的能量原理包含有力学和热力学原理两大部分.经典的小变形力学和可逆平衡态热力学理论巳不足于描述活体的运动.本文从大变形非对称应力理论力学描述活体宏观运动的力学能量原理.有关不可逆热力学问题将另文讨论.     

混凝土材料的粘塑性损伤本构模型

基于不可逆热力学,引入运动硬化、等向硬化和损伤内变量,构造了相应的自由能函数和流动势函数,推导出了混凝土材料的粘塑性损伤本构模型．数值模拟的结果表明,该模型能够避开屈服面和破坏准则的基本假设来描述混凝土材料的以下特性:压缩载荷作用下的体积膨胀现象;应变率敏感性;峰值后由损伤和破坏引起的应力软化和刚度退化现象A·D2由于此模型避开了根据各种变形阶段选择与其相应的本构模型的繁琐计算,因此更便于纳入复杂工况下应力分析有限元程序中．     

The pseudo‐elastic response of rubberlike solids

In this paper we focus on the mechanical behaviour of filled natural rubber. Filled elastomers under cyclic loading show noticeable differences between the mechanical response under loading and unloading during the first cycles in oscillation tests. We examine the change in material response associated with the Mullins effect and with cavitation, the latter arising from hydrostatic tensile stresses of sufficient magnitude. Then, we focus on constitutive equations using the theory of pseudoelasticity. Specifically, the strain‐energy function depends on a scalar parameter, which provides a means for modifying the form, thereby reflecting stress softening observed during unloading. The dissipation of energy is also accounted for by the use of a dissipation function, which evolves with the deformation history. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relaxed energy densities for large deformations of membranes

Tension field theory can be incorporated into the ordinary theoryof finite deformations of membranes by replacing the strainenergy function W with a certain relaxed energy density W_r.If W is a convex function of the strain, W_r is the largest convexand increasing function that does not exceed W, and W_r is aconvex function of the deformation gradient. Minimum energyand minimum complementary energy theorems are proved for thetheory based on W_r.